Problem 3 ( Solow Model combined with the Malthusian Model) Consider a Solow economy with the following production function F(K,N) = zK1f3N213 and parameters of = 0.05, s = 0.2, N9 = 100 and z = 1.0. Suppose K = 300 in period 0 and the Imit period is one year. In contrast to the standard Solow model, we assume that the population growth rate it is no longer exogenous but rather endogenous and determined by (1 + n) = Nf/N = rim/N) = (Cle3 as it is the case in the Malthusian model. 1. Determine the dynamics for the per worker capital (k). 2. Determine the per capita quantities k, 1 , r: and the aggregate quantities K, C and Y of the capital stock, consumption and output for years 1, 2 ,3, 4 and 5. Summarize your results using a table . 3. Find 13* the steady state pereapita capital stock, consmnption per capita (6*) and output per capita. (gt). 4. Show that in the steady state1 the population grows at a constant rate. Find this rate'.Fl